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topic 11
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- 1Describing associationsfor 2 continuous variables - can visualize using scatter plots, through this we can see the overall trend and variability of the relationship. Focus on 3 attributes:
1. direction (positive or negative)
2. Linearity (linear or non linear)
3. Strength (strong or weak)
After observing these we can use a correlation coefficient, or regression coefficient to find out if the observations are significant - 2Pearson correlationa correlation coefficient = measure of association that we can report, usually denoted by r
- unitless measure which ranges from -1 to +1
- correlation of +1 = perfect linear association
- correlation of -1 = perfect negative linear association
- correlation of 0 suggests no association
- the magnitude or absolute value represents the strength of the association, closer to 1 is stronger, closer to 0 is weaker
- + or - represents the direction of the association
- the null hypothesis would test that the Pearson correlation is 0 meaning no association
- based on means and SDs so will be affected by outliers
- only measures linear associations - 3Spearman Correlation- works by ranking each variable separately and seeing how closely ranks match upe.g. for a perfect linear correlation would be 1, as the smallest x would also be the smallest y etc.
- does not have to be linear, any monotonic relationship where the variables tend to change together will give a high spearman's value
- useful for evaluating relationships involving ordinal variables
- using ranks helps make Spearman's robust against outliers - 4Least Squares line- a Loess curve is a nonparametric method that tries to follow the trend in the data, making it a useful starting point in understanding the relationship
- fitting a line means choosing an intercept and slope to give a line that describes the trend in the data
- choose the line that minimizes the sum of the squared deviations from the line
- linear regression tells us how likely it is to get a least squares slope of x by chance, if the underlying slope really was 0 - uses a t statistic, is more than p<.001 then very strong evidence
- linear models can also be used to make predictions, this is an advantage over using correlation coefficients. Both approaches can be used to test association, but linear regression can make predictions as well - 5assumptions for linear regression1. independent observations
2. linear association
3. normal variability
4. constant variability , refers to constant variability of points from the line, rather than within distinct groups - 6checking assumptions for linear regressioncan check assumptions by exploring residuals - the difference between an observed response and the value predicted for the response by our model
- 7assumption for normal variability and constant variabilityessentially assumptions about how residuals should look
- constant variability: we can calculate the residuals for each observation and plot them against the x axis, this plot is also used to the linearity assumption, since the residuals are the values with the straight line removed. If the relationship is linear, there should be an obvious trend when you plot the residuals
- to test normality: make a histogram. A more advanced method is a probability plot, if the data is normal then values should lie close to the diagonal line - 8which method is best?- Correlation is useful as a simple test of association and is easy to interpret, working well for testing association between numerous pairs of variables
- linear regression is useful if you want to model your dependent variable and make predictions, particularly when you have multiple independent variables
- analysis of variance is a very general approach that can asses whether an overall model is significant and can be used to compare models
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- HRSS3101 Fichas sobre topic 11, creado por Soph B el 24/06/2020.
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- Soph B
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